• Title/Summary/Keyword: coulomb friction

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Formulation for seismic response of a ship-block system

  • Kuchaksarai, Masoud Moghaddasi;Bargi, Khosrow
    • Structural Engineering and Mechanics
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    • v.23 no.3
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    • pp.293-308
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    • 2006
  • This paper presents a complete and consistent formulation to study the seismic response of a free-standing ship supported by an arrangement of n keel blocks which are all located in a dry dock. It is considered that the foundation of the system is subjected to both horizontal and vertical in plane excitation. The motion of the system is classified in eight different modes which are Rest (relative), Sliding of keel blocks, Rocking of keel blocks, Sliding of the ship, Sliding of both keel blocks and the ship, Sliding and rocking of keel blocks, Rocking of keel blocks with sliding of the ship, and finally Sliding and rocking of keel blocks accompanied with sliding of the ship. For each mode of motion the governing equations are derived, and transition conditions between different modes are also defined. This formulation is based on a number of fundamental assumptions which are 2D idealization for motion of the system, considering keel blocks as the rigid ones and the ship as a massive rigid block too, allowing the similar motion for all keel blocks, and supposing frictional nature for transmitted forces between contacted parts. Also, the rocking of the ship is not likely to take place, and the complete ship separation from keel blocks or separation of keel blocks from the base is considered as one of the failure mode in the system. The formulation presented in this paper can be used in its entirety or in part, and they are suitable for investigation of generalized response using suitable analytical, or conducting a time-history sensitivity analysis.

A Two-Degree-of-Freedom-Controller for DC Motors Using Inverse Dynamics and the Fuzzy Technique (역동력학과 퍼지기법을 이용한 DC 모터용 2자유도 제어기)

  • Kim, Byong-Man;Kim, Jong-Hwa;Yu, Yung-Ho;Jin, Gang-Gyoo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.1
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    • pp.33-38
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    • 2002
  • In this paper, a Two-Degree-of-Freedom-Controller(TDFC) for DC motors based on inverse dynamics and the fuzzy technique is presented. The proposed controller includes the inverse dynamic model of a DC motor system, a prefilter and a fuzzy compensator. The model of the system is characterized by a nonlinear equation with coulomb friction. The prefilter eliminates high frequency effects occurring when the inverse dynamic model is implemented. The fuzzy compensator is designed for tracking the change of the reference input and simultaneously regulating the error between the reference input and the system output which can be caused by disturbances. The optimal parameters of both the model and the compensator are identified by a real-coded genetic algorithm. An experimental work on a DC motor system is carried out to verify the performance of the proposed controller.

A Study on the Joint Controller for a Humanoid Robot based on Genetic Algorithm (유전 알고리즘을 이용한 휴머노이드 로봇의 관절 제어기에 관한 연구)

  • Kong, Jung-Shik;Kim, Jin-Geol
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.5
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    • pp.640-647
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    • 2007
  • This paper presents a joint controller for a humanoid robot based on genetic algorithm. h humanoid robot has basically instability during walking because it isn't fixed on the ground. Moreover nonlinearities of the joints increase its instability. If one of them isn't satisfied, the robot may fall down at the ground during walking. To attack one of those problems, joint controller is proposed. It can perform tracking control preciously and reduce the effect of nonlinearities by gear, limitation of the input voltage, coulomb friction and so on. This controller is based on fuzzy-sliding mode controller (FSMC) and compensator and control gains are searched by a proposed genetic algorithm. It can reduce the effect by nonlinearities. Also, to improve the tracking performance, the proposed controller has motion controller. From the given controller, a humanoid robot can moved more preciously. Here, all the processes are investigated through simulations and it is verified experimentally in a real joint system for a humanoid robot.

Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

  • Nagy, N.;Mohamed, M.;Boot, J.C.
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.1-18
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    • 2010
  • The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

Theoretical model for the shear strength of rock discontinuities with non-associated flow laws

  • Galindo, Ruben;Andres, Jose L.;Lara, Antonio;Xu, Bin;Cao, Zhigang;Cai, Yuanqiang
    • Geomechanics and Engineering
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    • v.24 no.4
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    • pp.307-321
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    • 2021
  • In an earlier publication (Serrano et al. 2014), the theoretical basis for evaluating the shear strength in rock joints was presented and used to derive an equation that governs the relationship between tangential and normal stresses on the joint during slippage between the joint faces. In this paper, the theoretical equation is applied to two non-linear failure criteria by using non-associated flow laws, including the modified Hoek and Brown and modified Mohr-Coulomb equations. The theoretical model considers the geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness as dependent variables. This model uses a similar equation structure to the empirical law that was proposed by Barton in 1973. However, a good correlation with the empirical values and, therefore, Barton's equation is necessary to incorporate a non-associated flow law that governs breakage processes in rock masses and becomes more significant in highly fractured media, which can be induced in a rock joint. A linear law of dilatancy is used to assess the importance of the non-associated flow to obtain very close values for different roughness states, so the best results are obtained for null material dilatancy, which considers significant changes that correspond to soft rock masses or altered zones of weakness.

Seismic Performance of Bridges with the Modeling of Expansion Rocker Bearings (라커베어링 모델에 따른 교량의 지진거동)

  • Choi, Eunsoo
    • Journal of Korean Society of Steel Construction
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    • v.14 no.6
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    • pp.755-763
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    • 2002
  • Multispan simply supported bridges and multispan continuous bridges take a large portion of bridges in Central and Southeastern United Sates. The superstructure of the bridges are supported by steel rocker bearings. In general, the rocker bearings are modeled with ideal rollers or Coulomb fricition in seismic analysis. However, the rocker bearings have rocking action on pintles after rolling some distance. This rocking action may have considerable effect on the seismic performance of bridges. This study compares the effect of expansion rocker bearings models on a multispan simply supported and a multispan continuous bridge. Since the ideal roller model produces larger responses than the rocking model, its use is undesirable. However, the fricition and hardening model does not have much difference from the responses of the rocking model. In addition, the use of the tow models is convenient in seismic analyses of bridges. Although the rocking model can obtain more exact responses, its behavior is complicated and it may induce the conversion problem in time history analysis because it includes the abrupt changing of stiffiness. The friction and hardening model of expansion rocker bearings is therefore recommended in sesismic analysis.

A Study on the Stability of Deep Tunnels Considering Brittle Failure Characteristic (취성파괴특성을 고려한 심부터널의 안정성 평가기법 연구)

  • Park, Hyun-Ik;Park, Yeon-Jun;You, Kwang-Ho;Noh, Bong-Kun;Seo, Young-Ho;Park, Chan
    • Tunnel and Underground Space
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    • v.19 no.4
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    • pp.304-317
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    • 2009
  • Most crystalline rocks have much higher compressive strength than tensile strength and show brittle failure. In-situ rock mass, strong enough in general sense, often fails in brittle manner when subjected to high stress exceeding strength in due of geometrically induced stress concentration or of high initial stress. Therefore, it is necessary to verify the brittle failure characteristics of rock and rock mass for proper stability assessment of underground structures excavated in great depths. In this study, damage controlled tests were conducted on biotite-granite and granitic gneiss, which are the two major crystalline rock types in Korea, to obtain the strain dependency characteristics of the cohesion and friction angle. A Cohesion-Weakening Friction-Strengthening (CWFS hereafter) model for each rock type was constructed and a series of compression tests were carried out numerically while varying confining pressures. The same tests were also conducted assuming the rock is Mohr-Coulomb material and results were compared.

A Study on Estimating Shear Strength of Continuum Rock Slope (연속체 암반비탈면의 강도정수 산정 연구)

  • Kim, Hyung-Min;Lee, Su-gon;Lee, Byok-Kyu;Woo, Jae-Gyung;Hur, Ik;Lee, Jun-Ki
    • Journal of the Korean Geotechnical Society
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    • v.35 no.5
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    • pp.5-19
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    • 2019
  • Considering the natural phenomenon in which steep slopes ($65^{\circ}{\sim}85^{\circ}$) consisting of rock mass remain stable for decades, slopes steeper than 1:0.5 (the standard of slope angle for blast rock) may be applied in geotechnical conditions which are similar to those above at the design and initial construction stages. In the process of analysing the stability of a good to fair continuum rock slope that can be designed as a steep slope, a general method of estimating rock mass strength properties from design practice perspective was required. Practical and genealized engineering methods of determining the properties of a rock mass are important for a good continuum rock slope that can be designed as a steep slope. The Genealized Hoek-Brown (H-B) failure criterion and GSI (Geological Strength Index), which were revised and supplemented by Hoek et al. (2002), were assessed as rock mass characterization systems fully taking into account the effects of discontinuities, and were widely utilized as a method for calculating equivalent Mohr-Coulomb shear strength (balancing the areas) according to stress changes. The concept of calculating equivalent M-C shear strength according to the change of confining stress range was proposed, and on a slope, the equivalent shear strength changes sensitively with changes in the maximum confining stress (${{\sigma}^{\prime}}_{3max}$ or normal stress), making it difficult to use it in practical design. In this study, the method of estimating the strength properties (an iso-angle division method) that can be applied universally within the maximum confining stress range for a good to fair continuum rock mass slope is proposed by applying the H-B failure criterion. In order to assess the validity and applicability of the proposed method of estimating the shear strength (A), the rock slope, which is a study object, was selected as the type of rock (igneous, metamorphic, sedimentary) on the steep slope near the existing working design site. It is compared and analyzed with the equivalent M-C shear strength (balancing the areas) proposed by Hoek. The equivalent M-C shear strength of the balancing the areas method and iso-angle division method was estimated using the RocLab program (geotechnical properties calculation software based on the H-B failure criterion (2002)) by using the basic data of the laboratory rock triaxial compression test at the existing working design site and the face mapping of discontinuities on the rock slope of study area. The calculated equivalent M-C shear strength of the balancing the areas method was interlinked to show very large or small cohesion and internal friction angles (generally, greater than $45^{\circ}$). The equivalent M-C shear strength of the iso-angle division is in-between the equivalent M-C shear properties of the balancing the areas, and the internal friction angles show a range of $30^{\circ}$ to $42^{\circ}$. We compared and analyzed the shear strength (A) of the iso-angle division method at the study area with the shear strength (B) of the existing working design site with similar or the same grade RMR each other. The application of the proposed iso-angle division method was indirectly evaluated through the results of the stability analysis (limit equilibrium analysis and finite element analysis) applied with these the strength properties. The difference between A and B of the shear strength is about 10%. LEM results (in wet condition) showed that Fs (A) = 14.08~58.22 (average 32.9) and Fs (B) = 18.39~60.04 (average 32.2), which were similar in accordance with the same rock types. As a result of FEM, displacement (A) = 0.13~0.65 mm (average 0.27 mm) and displacement (B) = 0.14~1.07 mm (average 0.37 mm). Using the GSI and Hoek-Brown failure criterion, the significant result could be identified in the application evaluation. Therefore, the strength properties of rock mass estimated by the iso-angle division method could be applied with practical shear strength.